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Abstract:

A 4D seismic technique, where a base seismic trace is measured at a first
time in a region of the subsoil, and then a monitor seismic trace
corresponding to the base seismic trace is measured at a second time. To
interpret the 4D measurements, assumptions are made about the variation
of elastic parameters in permeable layers at predefined positions in one
direction between the first and the second time. Elastic parameters
include the density (ρ) and the speed of propagation of the pressure
waves (VP) in the permeable layers. Numerical evaluation is
performed for a capability of each assumption about the variation of
elastic parameters to give an account of a change between the measured
base seismic trace and the measured monitor seismic trace, and the
variation of the elastic parameters is estimated in accordance with an
assumption of optimum capability.

Claims:

1. A method for estimating elastic parameters of a region of the subsoil,
comprising: measuring at least one base seismic trace in a first phase;
measuring, in a second phase, at least one monitor seismic trace
corresponding to the base seismic trace; making assumptions of variation
of elastic parameters in permeable layers of predefined positions along a
direction between the first and the second phases, the elastic parameters
including a density (ρ) and a speed of propagation of pressure waves
(VP) in each of said permeable layers; numerically evaluating a
capacity of each assumption of variation of elastic parameters to account
for an evolution between the measured base seismic trace and the measured
monitor seismic trace; and estimating the variation of the elastic
parameters in accordance with an assumption having an optimum evaluated
capacity.

2. The method as claimed in claim 1, wherein the base and monitor seismic
traces are measured by sending seismic waves at normal incidence toward
layers following one another along said direction and by collecting the
seismic waves reflected by interfaces between said layers.

3. The method as claimed in claim 1, wherein the base and monitor seismic
traces are measured by sending seismic waves at non-normal incidence
toward layers following one another along said direction and by
collecting the seismic waves reflected by the interfaces between said
layers, and wherein the elastic parameters also include a speed of
propagation of shear waves (VS) in the permeable layers along said
direction.

4. The method as claimed in claim 1, wherein the elastic parameters
further include the position, along said direction, of at least one
interface delimiting one of said permeable layers.

5. The method as claimed in claim 1, wherein the variations of elastic
parameters are taken into account in permeable layers along a well
drilled in the subsoil.

6. The method as claimed in claim 5, wherein the positions of the
permeable layers along the well are defined on the basis of measurements
performed in the well.

7. The method as claimed in claim 5, wherein the positions of the
permeable layers along the well are defined on the basis of positions of
perforations made in a casing of the well.

8. The method as claimed in claim 5, wherein the numerical evaluation of
the capacity of an assumption of variation of elastic parameters to
account for the evolution between the measured base seismic trace and the
measured monitor seismic trace comprises: computing a simulated base
seismic trace on the basis of a wavelet representative of an incident
seismic signal and of values of the elastic parameters measured in the
well in the first phase; obtaining values of the elastic parameters in
the well for the second phase on the basis of the values measured in the
well in the first phase and of said assumption of variation; computing a
simulated monitor seismic trace on the basis of said wavelet and of the
values of the elastic parameters in the well obtained for the second
phase; and comparing a difference between the measured monitor seismic
trace and the measured base seismic trace with a difference between the
simulated monitor seismic trace and the simulated base seismic trace.

9. The method as claimed in claim 5, wherein the numerical evaluation of
the capacity of an assumption of variation of elastic parameters to
account for the evolution between the measured base seismic trace and the
measured monitor seismic trace comprises: obtaining values of the elastic
parameters in the well for the second phase on the basis of values of the
elastic parameters measured in the well in the first phase and of said
assumption of variation; estimating a perturbation in amplitude of the
measured base seismic trace resulting from a change of the elastic
parameters in the well from the values measured in the first phase to the
values obtained for the second phase; computing a seismic pseudo-trace by
combining one of the measured seismic traces with the estimated amplitude
perturbation; and comparing, on a same timescale, the other one of the
measured seismic trace with the computed seismic pseudo-trace.

10. The method as claimed in claim 9, wherein the estimation of the
amplitude perturbation comprises: computing a simulated base seismic
trace on the basis of a wavelet representative of an incident seismic
signal and of values of the elastic parameters measured in the well in
the first phase; computing a simulated monitor seismic trace on the basis
of said wavelet and of values of the elastic parameters in the well
obtained for the second phase, the simulated base and monitor seismic
traces being computed with a same depth-time conversion law; and
subtracting the simulated base seismic trace from the simulated monitor
seismic trace to obtain the estimated amplitude perturbation.

11. The method as claimed in claim 1, wherein the numerical evaluation of
the capacity of an assumption of variation of the elastic parameters to
account for the evolution between the measured base seismic trace and the
measured monitor seismic trace comprises: estimating a perturbation in
amplitude of the measured base seismic trace resulting from the variation
of the elastic parameters; computing a seismic pseudo-trace by combining
one of the measured seismic traces with the estimated amplitude
perturbation; and comparing, on a same timescale, the other one of the
measured seismic traces with the computed seismic pseudo-trace.

12. The method as claimed in claim 11, wherein the amplitude perturbation
is estimated as a function of impedance variations in said permeable
layers, deduced from the assumption of variation of the elastic
parameters, and from a wavelet representative of an incident seismic
signal.

13. The method as claimed in claim 9, wherein the measured seismic trace
combined with the estimated amplitude perturbation for the computation of
the seismic pseudo-trace is the measured monitor seismic trace, the
combination comprising: modifying the timescale of the measured monitor
seismic trace to take into account a variation of speed of propagation of
the seismic waves in accordance with the assumption of variation of
elastic parameters; and subtracting the estimated amplitude perturbation
from the modified measured monitor seismic trace.

14. The method as claimed in claim 1, wherein the positions of the
permeable layers along said direction are defined on the basis of a
reservoir grid.

15. The method as claimed in claim 11, wherein the measured seismic trace
combined with the estimated amplitude perturbation for the computation of
the seismic pseudo-trace is the measured monitor seismic trace, the
combination comprising: modifying the timescale of the measured monitor
seismic trace to take into account a variation of speed of propagation of
the seismic waves in accordance with the assumption of variation of
elastic parameters; and subtracting the estimated amplitude perturbation
from the modified measured monitor seismic trace.

Description:

PRIORITY CLAIM

[0001] The present application is a National Phase entry of PCT
Application No. PCT/FR2011/051720, filed Jul. 19, 2011, which claims
priority from French Application Number 10 55945, filed Jul. 21, 2010,
the disclosures of which are hereby incorporated by reference herein in
their entirety.

BACKGROUND OF THE INVENTION

[0002] The present invention relates to the geophysical methods employed
to estimate parameters of the subsoil, notably in the context of
hydrocarbon exploration and production.

[0003] It relates more particularly to the so-called 4D seismic
techniques. In these techniques, there are first seismic recordings,
obtained in a first phase during a campaign of "base" measurements ("base
survey"), for example before a hydrocarbon reservoir is placed in
production, and there is a subsequent campaign of measurements ("monitor
survey"), for example after a few years of operation of the reservoir, to
obtain second seismic recordings. The base and monitor seismic recordings
(or seismic traces) are compared to estimate variations of physical
parameters of the geological layers in the area explored.

[0004] The parameters of which the variations are thus estimated may
comprise the density ρ, the speed VP of propagation of the
pressure waves (P waves) and the speed VS of propagation of the
shear waves (S waves) in the media forming the various geological layers
of the area explored. Reference is often made to the seismic impedances
in each medium, IP=ρ×VP and
IS=ρ×VS, which govern the propagation of the P waves
and S waves in the layers. Because of the changes linked to oil
production, for example the replacement of oil with water or gas, the
parameters ρ, VP, VS are modified in certain layers. This
results in changes of amplitude in the seismic recordings, and in time
offsets in the recorded seismic traces. The comparative analysis of the
recordings comprises an inversion to estimate the variations of the
parameters in order to obtain an idea of the levels of saturation in the
layers being operated.

[0005] An inversion method that can be used to analyze the time offsets in
the base and monitor seismic traces (dependant on the variations of
propagation speeds) at the same time as the changes of amplitude
(dependant on the impedance variations) is described in EP 1 865 340 A1.

[0006] A 3D seismic technique, i.e. a technique based on a single survey,
taking into account well logs is described in the U.S. Pat. No.
5,798,982, which also mentions an extension of the technique to 4D
seismic by a comparison of inverted seismic blocks.

[0007] Another 4D seismic data analysis method, described in WO
2008/140655 A1, uses a model-based inversion in one or more wells where
logs have been recorded. The document does not describe the inversion
method or the way in which the model is parameterized. The results of the
inversion are then extended by moving away from the well, using a
statistical method. A correlation computation is performed in order to
relate the time reference of the monitor recordings to that of the base
recordings. With the model used, the method seeks to directly estimate
variations of saturation levels and pressure variations in the geological
layers.

[0008] An object of the invention is to add to the 4D seismic techniques,
notably by making them take into account geological and dynamic
constraints.

SUMMARY OF THE INVENTION

[0009] There is proposed a method for estimating elastic parameters of a
region of the subsoil, comprising:

[0010] measuring at least one base
seismic trace in a first phase;

[0011] measuring, in a second phase, at
least one monitor seismic trace corresponding to the base seismic trace;

[0012] making assumptions of variation of elastic parameters in permeable
layers of predefined positions along a direction between the first and
the second phases, the elastic parameters including a density and a speed
of propagation of pressure waves in each of said permeable layers;

[0013]
numerically evaluating a capacity of each assumption of variation of
elastic parameters to account for an evolution between the measured base
seismic trace and the measured monitor seismic trace;

[0014] estimating
the variation of the elastic parameters in accordance with an assumption
having an optimum evaluated capacity.

[0015] The technique uses a geological-dynamic a priori to estimate the 4D
parameters on the reservoir scale. This estimation is performed along a
predefined direction, generally vertical. It can be the direction of a
well drilled in the area studied or, in certain situations, a direction
chosen arbitrarily without having to be located along a well.

[0016] When the propagation speeds that are being estimated are limited to
the speed of propagation of the pressure waves VP, the base and
monitor seismic traces can be measured by sending seismic waves at normal
incidence toward layers following one another along said direction and by
collecting the seismic waves reflected by interfaces between said layers.
The method can also be extended to the estimation of the speeds of
propagation of the shear waves in the permeable layers, the base and
monitor seismic traces then being measured by sending seismic waves at
non-normal incidence toward layers following one another along said
direction and by collecting the seismic waves reflected by the interfaces
between said layers. The elastic parameters of which the variations are
being tested can also include the position, along said direction, of at
least one interface delimiting one of said permeable layers.

[0017] In one embodiment of the method, the variations of elastic
parameters are taken into account in permeable layers along a well
drilled in the subsoil. The permeable layers are typically positioned
along said direction, which is then the direction of drilling of the
well, on the basis of measurements (logs) performed in the well. Another
possibility, if the well is in operation, is to define the positions of
the permeable layers along the well on the basis of positions of
perforations made in a casing of the well.

[0018] For a well that is in operation, it is commonplace to have
available a reservoir grid that is used by the reservoir engineers to
predict production. A reservoir grid is constructed by a geomodeling
technique based on structural information derived from the seismic
recordings and from the wells. This grid is filled with the physical
properties of the rocks, notably the permeability and porosity,
calibrated on the well data. Typically, a certain number of wells are
drilled in the area placed in operation, and the data obtained from the
logs are interpolated between wells to establish a first grid which is
then refined using seismic recordings. In the context of the present
invention, the reservoir grid can be used to provide the geological a
priori used in the 4D inversion.

[0019] The positions of the permeable layers along the abovementioned
direction are then defined on the basis of the reservoir grid. It should
be noted that this makes it possible to implement the method in a well,
the values of elastic parameters for which the variations are being
tested being those located along the well in the reservoir grid, but also
in the absence of wells. In this latter case, the permeable layers where
the elastic parameters are estimated are those that said direction
encounters in the reservoir grid. If the resolution of the reservoir grid
is too fine, it is possible to aggregate a plurality of layers thereof in
a single permeable layer taken into account in the 4D inversion.

[0020] A certain number of approaches are possible for the numerical
evaluation of the capacity of an assumption of variation of elastic
parameters to account for the evolution between the measured base seismic
trace and the measured monitor seismic trace.

[0021] When the elastic parameters are estimated along a well, it is
possible to obtain, for each assumption of variation, values of the
elastic parameters in the well for the second phase on the basis of
values of the elastic parameters measured in the well in the first phase
(logs). According to one approach, a simulated base seismic trace is
computed on the basis of a wavelet representative of an incident seismic
signal and of the values of the elastic parameters measured in the well
in the first phase, a simulated monitor seismic trace is computed on the
basis of said wavelet and of the values of the elastic parameters in the
well obtained for the second phase, and the difference between the
measured monitor seismic trace and the measured base seismic trace is
compared with the difference between the simulated monitor seismic trace
and the simulated base seismic trace. If the comparison reveals that a
predetermined condition is fulfilled (for example, the difference between
the two trace differences is below a threshold, or is the lowest observed
for a set of assumptions of variation tested), the assumption of
variation that is considered to have an optimum capacity is retained for
the estimation of the elastic parameters in the second phase (monitor).

[0022] In another approach, an amplitude perturbation of the measured base
seismic trace resulting from a change of the elastic parameters in the
well from the values measured in the first phase to the values obtained
for the second phase is estimated, a seismic pseudo-trace is computed by
combining one of the measured seismic traces with the estimated amplitude
perturbation, and, on a same timescale, the other one of the measured
seismic traces is compared with the computed seismic pseudo-trace. The
result of the comparison can then be used to decide on the estimation of
the elastic parameters.

[0023] The estimation of the perturbation in amplitude can use the logs
recorded before the well is put into operation (base time). It then
comprises the computation of a simulated base seismic trace on the basis
of a wavelet representative of an incident seismic signal and of the
values of the elastic parameters measured in the well in the first phase,
the computation of a simulated monitor seismic trace on the basis of said
wavelet and of the values of the elastic parameters in the well obtained
for the second phase, the simulated base and monitor seismic traces being
computed with one and the same depth-time conversion law, and a
subtraction between the simulated base seismic trace and the simulated
monitor seismic trace to obtain the estimated amplitude perturbation.

[0024] Yet another approach can be adopted with or without the presence of
a well. It consists in estimating a perturbation in amplitude of the
measured base seismic trace resulting from the variation of the elastic
parameters, in computing a seismic pseudo-trace by combining one of the
measured seismic traces with the estimated amplitude perturbation, and in
comparing, on one and the same timescale, the other of the measured
seismic traces with the computed seismic pseudo-trace. The amplitude
perturbation can be estimated approximately as a function of impedance
variations in the permeable layers, deduced from the assumption of
variation of the elastic parameters, and from a wavelet representative of
an incident seismic signal.

[0025] In one embodiment, the capacity of an assumption of variation of
elastic parameters to account for the evolution between the measured base
seismic trace and the measured monitor seismic trace is evaluated
numerically by relating to the base reference frame the monitor seismic
trace deformed as a function of the assumptions of variation of the
elastic parameters. The measured seismic trace that is combined with the
estimated amplitude perturbation for the computation of the seismic
pseudo-trace is then the measured monitor seismic trace, and the
combination comprises modifying the timescale of the measured monitor
seismic trace to take into account the variation of speed of propagation
of the seismic waves in accordance with the assumption of variation of
elastic parameters, and obtaining the seismic pseudo-trace by subtracting
the estimated amplitude perturbation from the modified measured monitor
seismic trace.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Other features and advantages of the present invention will become
apparent in the following description of a nonlimiting exemplary
embodiment, with reference to the appended drawings, in which:

[0027] FIG. 1 is a diagram illustrating a seismic measurement mode near a
well;

[0028]FIG. 2 is a diagram illustrating synthesis of a seismic trace on
the basis of measurements performed in a well (logs);

[0029]FIG. 3 is a diagram illustrating the evolution from a base seismic
trace to a monitor seismic trace as a function of an assumption of
variation of the density and of the speed of propagation of the pressure
waves in the permeable layers along the well;

[0030]FIG. 4 is a diagram illustrating a first embodiment of the method
for estimating elastic parameters according to the invention;

[0031] FIGS. 5 and 6 are diagrams illustrating two other embodiments of
the method;

[0032]FIG. 7 is a diagram illustrating another way of acquiring a seismic
trace that can be used in an embodiment of the method.

DESCRIPTION OF EMBODIMENTS

[0033] FIG. 1 illustrates an oil production area where a well 10 has been
drilled. This well 10 passes through layers, represented very
diagrammatically in FIG. 1, that have variable elastic parameters.

[0034] Before the casing of the well is put in place, a number of
measurements (logs) have been carried out therein in order to know, with
a resolution of the order of a few tens of centimeters, the values of
different physical parameters of the rocks passed through by the well.
These parameters notably include the porosity, the permeability, the
density and the speed of propagation of the pressure waves. The left hand
part of FIG. 2 shows an exemplary recording of the speed VP of
propagation of the pressure waves and of the density ρ of the rocky
formations as a function of depth along the well.

[0035] In a seismic survey in the region considered, a source of seismic
waves 11 is successively placed at different places on the surface, or in
the sea in the case of an offshore area, and one or more seismic wave
detectors 12 collect the seismic waves originating from the source 11
which are reflected on the interfaces between the geological layers
encountered. FIG. 1 illustrates the particular case in which the source
11 and the detector 12 are placed in immediate proximity to the well 10
in order to record seismic waves which are propagated vertically along
the well with an approximately normal incidence on the interfaces between
layers.

[0036] In this configuration, the amplitude of the seismic signal
collected by the detector 12 can be modeled by a convolution of the
seismic impedance IP=ρ×VP relative to the pressure
waves with a wavelet w(t) representing the wave form of the signal
emitted by the source 11:

[0037] This modeling is illustrated by FIG. 2 where the first step
consists in converting the logs VP(z), ρ(z) obtained as a
function of the depth in the well into logs VP(t), ρ(t)
expressed as a function of the propagation time of the waves to be able
to be convolved according to (1). The depth-time conversion law used for
that is directly deduced from the evolution of the speed VP along
the well. The convolution of the impedance IP=ρ×VP by
the wavelet W(t) makes it possible to synthesize a seismic trace A(t)
represented in the right hand part of FIG. 2.

[0038] In general, it is possible to obtain the profile of the parameters
VP and ρ along the well using the logs initially performed, i.e.
performed in the base time. However, in the 4D seismic monitor time
(typically a few years after the base time), there is no longer access to
the wall of the well to be able to measure therein the values of VP
and ρ which might have changed because of the production.

[0039] However, assumptions can be formulated as to the variations
ΔVP and Δρ of the parameters between the base time
and the monitor time and the capacity of these assumptions of variation
to account for the modifications of the seismic traces recorded in
conditions similar to the base time and to the monitor time can be
tested. It is convenient to express these parameter variations in a
relative manner, namely in the form ΔVP/VP and
Δρ/ρ.

[0040] In general, it is in the permeable layers encountered along the
well that the parameters VP and ρ will have changed most
significantly because it is in these layers that the oil extracted from
the subsoil flows during operation. In the left hand part of FIG. 3, two
permeable layers 20, 30 are represented in which the speed VP and
the density ρ have been able to change between the base time and the
monitor time, an assumption of variation ΔVP/VP and
Δρ/ρ being indicated in these layers (in practice, the
number of these layers is much greater than 2). It is then possible to
synthesize a simulated base seismic trace AB(t) and a simulated
monitor seismic trace AM(t):

[0041] The change in the density ρ and the speed VP as a result
of the oil production has two effects on the modeling:

[0042] a change
in the depth-time relationship used for the conversion of the logs
ρ(z)→ρ(t) and VP(z)→VP(t);

[0043] a
change of amplitude due to the change of impedance as indicate by the
above formula (3).

[0044] From these expressions (2) and (3), it is possible to check whether
the assumption of variation ΔVP/VP and Δρ/ρ
properly accounts for the evolution observed between two seismic traces
AB(t), AM(t) successively measured at the base time and at the
monitor time.

[0045]FIG. 4 illustrates a first way of carrying out this check. The left
hand part of FIG. 4 shows the logs VP(t) and ρ(t) measured as a
function of the depth at the base time and converted to be expressed as a
function of the propagation time, as well as a number of assumptions
ΔVP/VP, Δρ/ρ of variation of the parameters
in the permeable layers 20, 30.

[0046] Using the scheme illustrated by FIG. 3, base and monitor simulated
seismic traces AB(t), AM(t) are obtained, then their difference
ΔA(t)=AM(t)-AB(t) is computed. This difference
ΔA(t) is compared to the difference
ΔA(t)=ΔAM(t)-AB(t) between the measured base and
monitor traces. The difference ΔA(t)-ΔA(t) is minimized as a
function of the assumptions of variation ΔVP/VP,
Δρ/ρ in order to select the assumption which accounts best
for the evolution in the seismic trace. The optimization may consist in
scanning a large number of assumptions ΔVP/VP,
Δρ/ρ and in retaining the one that provides the smallest
average value of |ΔA(t)-ΔA(t)| or
[ΔA(t)-ΔA(t)]2, or which minimizes another distance
measurement between ΔA(t) and ΔA(t). Another possibility is
to select an assumption ΔVP/VP, Δρ/ρ when
the time average of |ΔA(t)-ΔA(t)| is below a predefined
threshold.

[0047] Various minimization algorithms can be applied, for example genetic
or simulated annealing algorithms, which do not require any computation
of gradients and are not trapped in local minima.

[0048] The cost function |ΔA-ΔA| is not necessarily the best
for performing the optimization in as much as the synthetic base trace
often has an appearance that is quite different from the measured base
trace. In practice, it is often more appropriate to transform one of the
measured traces into the reference frame of the other trace for each
assumption of variation before proceeding with a distance computation
between these two traces.

[0049] Such an embodiment is illustrated by FIG. 5, which shows, in the
left hand part, logs VP(t), ρ(t) as a function of time and an
assumption ΔVP/VP, Δρ/ρ of variation of the
parameters in the permeable layers 20, 30. FIG. 5 also shows a base
seismic trace AB(t) measured before the well is put into production.

[0050] From the logs VP(z) and ρ(z) and the assumptions of
variation ΔVP/VP, Δρ/ρ, a base synthetic
trace AB(t) and a base monitor synthetic trace AM(t) are
computed by applying the formulae (2) and (3) above. However, before
applying the formula (3), the depth-time conversion law applicable to the
base time (curve 15 in the z, t diagram of FIG. 5) is used to convert the
values

expressed as a function of the propagation time. The difference
ΔA(t)=AM(t)-AB(t) between the two synthetic traces is
then computed in the time reference frame of the base. This difference
ΔA(t) is then added to the measured base seismic trace AB(t)
to obtain a first monitor pseudo-trace A'M(t) represented in FIG. 5:
A'M(t)=AB(t)+ΔA(t).

[0051] This pseudo-trace A'M(t) is expressed in the time reference
frame of the base time. The timescale must be modified to relate the
pseudo-trace to the time reference frame of the monitor time and thus
obtain a second pseudo-trace A''M(t) represented in the right hand
part of FIG. 5. The change of timescale is performed in such a way as to
compensate for the difference between the depth-time conversion law
applicable to the base time (curve 15) and the depth-time conversion law
applicable to the monitor time (curve 16).

[0052] In the embodiment of FIG. 5, the optimization uses a cost function
given by the difference between the measured monitor seismic trace
AM(t) and the seismic pseudo-trace A''M(t) computed in the
manner described previously, for example the sum of the squares or the
sum of the absolute values of this difference.

[0053] It should be observed that there are a number of ways of relating
one of the traces to the reference frame of the other by taking into
account an assumption of variation of the parameters in order to perform
the optimization. An advantageous embodiment starts from the measured
monitor seismic trace to relate it to the reference frame of the base
seismic trace. In particular, it is possible to begin by modifying the
timescale of the measured monitor seismic trace AM(t) to relate it
to the scale applicable to the base time (compensation of the difference
between the curves 15 and 16). Then, the difference ΔA(t) computed
as previously is subtracted from the pseudo-trace obtained to obtain a
pseudo-trace A''B(t) expressed in the time reference frame
associated with the base time. The cost function involved in the
optimization is then given by the difference between this pseudo-trace
A''B(t) and the measured base seismic trace AB(t).

[0054]FIG. 6 illustrates an alternative embodiment implementing an
approximate method inspired by that of FIG. 5. In this approximate
method, no measured log is taken into consideration. Consequently, this
method can be applied independently of a well. It is notably applicable
for searching for the evolution of the parameters VP, ρ in
geological layers whose positioning along a typically vertical direction
is determined as a function of the reservoir grid determined for the
operation of the area considered.

[0055] In the method illustrated by FIG. 6, the modification ΔA(t)
of the base seismic trace expressed in the reference frame of the base
time is not computed on the basis of measured logs using the above
formulae (2) and (3). It is expressed directly as a function of the
impedance variation ΔIP/IP corresponding to the
assumption of variation of the propagation speed VP and of the
density ρ:

ΔIP/IP≈ΔVP/VP+Δρ/ρ
(4)

[0056] The relative variation of amplitude ΔA/A is estimated in an
approximate manner as being proportional to the relative impedance
variation ΔIP/IP, the proportionality coefficient being
the amplitude of the wavelet w(t) representing the incident seismic
signal.

[0057] Based on the perturbation ΔA(t) computed in an approximate
manner, the method illustrated by FIG. 6 continues by computing a first
monitor pseudo-trace A'M(t)=AB(t)+ΔA(t). As in the method
illustrated by FIG. 5, a second pseudo-trace A''M(t) is computed by
a change of timescale to be compared to the measured monitor seismic
trace AM(t). The result of the comparison is then used as cost
function for the optimization.

[0058] In FIG. 6, the trace 18 represented by dotted lines corresponds to
the first pseudo-trace A'M(t) computed without approximation in the
manner described with reference to FIG. 5. It can be seen that the
approximate pseudo-trace differs slightly from the latter around the
edges of the permeable layers.

[0059] In the case where the seismic waves are sent at normal incidence
toward the layers studied and are collected with no significant lateral
offset between the source 11 and the detector 12, the speed of
propagation of the pressure waves VP and the density ρ are
sufficient to model the propagation of the waves sensed by the detector
12.

[0060] The method described above is also applicable in the case where an
offset exists between the source 11 and the detector 12 as represented in
FIG. 7.

[0061] In this latter case, the impedance variation ΔIP/IP
involved in the approximate method illustrated by FIG. 6 depends also on
the speed of propagation of the shear waves VS through the angle
θ of incidence of the wave on the interface:

[0062] It can then be seen that it is possible to include the speed
VS of propagation of the shear waves in the elastic parameters taken
into account in the assumptions of variation. The method therefore gives
access to estimations of the speed VS. One possibility is to
evaluate VP and ρ in a first step on the basis of seismic traces
recorded at normal incidence (FIG. 1), and to then make assumptions of
variation of the parameters VS alone to perform the optimization as
a function of this parameter in a second step on the basis of seismic
traces recorded with offset.

[0063] The method described above in different embodiments takes advantage
of geophysical information (the seismic traces) and of information
commonly available to the reservoir engineers (the layer modeling of the
subsoil). It provides a novel way of analyzing 4D seismic data that makes
it possible to take into account a priori information as to the
geological and dynamic behavior of the area studied.

[0064] It will be understood that the invention is not limited to the
particular embodiments which have been described above, numerous variants
being able to be conceived without departing from the scope defined by
the attached claims.

[0065] The embodiments above are intended to be illustrative and not
limiting. Additional embodiments may be within the claims. Although the
present invention has been described with reference to particular
embodiments, workers skilled in the art will recognize that changes may
be made in form and detail without departing from the spirit and scope of
the invention.

[0066] Various modifications to the invention may be apparent to one of
skill in the art upon reading this disclosure. For example, persons of
ordinary skill in the relevant art will recognize that the various
features described for the different embodiments of the invention can be
suitably combined, un-combined, and re-combined with other features,
alone, or in different combinations, within the spirit of the invention.
Likewise, the various features described above should all be regarded as
example embodiments, rather than limitations to the scope or spirit of
the invention. Therefore, the above is not contemplated to limit the
scope of the present invention.